Several of Nadia's friends wanted to try the candy bars she brought back from her trip, but there were only 35 candy bars. Nadia decided to cut the candy bars into pieces so that each person could have $\frac{7}{8}$ of a candy bar. After cutting up the candy bars, how many friends could Nadia share her candy with?
Solution: We can divide the number of candy bars ( $35$ ) by the amount Nadia gave to each person ( $\frac{7}{8}$ of a bar) to find out how many people she could share with. $ \dfrac{{35 \text{ candy bars}}} {{\dfrac{7}{8} \text{ bar per person}}} = {\text{ total people}} $ Dividing by a fraction is the same as multiplying by the reciprocal. The reciprocal of $\dfrac{7}{8} \text{ bar per person}$ is ${\dfrac{8}{7} \text{ people per bar}}$ $ {35\text{ candy bars}} \times {\dfrac{8}{7} \text{ people per bar}} = {\text{total people}} $ ${\dfrac{280}{7}\text{ people}} = 40\text{ people}$ By cutting up the candy bars, Nadia could share her candy with 40 of her friends.